On computing givens rotations reliably and efficiently

DOI10.1145/567806.567809zbMath1072.65048OpenAlexW2061771449WikidataQ113309772 ScholiaQ113309772MaRDI QIDQ5461237

William Kahan, David Bindel, Osni A. Marques, James W. Demmel

Publication date: 22 July 2005

Published in: ACM Transactions on Mathematical Software (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1145/567806.567809

zbMATH Keywords

LAPACK routinesGivens rotationsCLARGVCLARTGSLARGSLARTG

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Complexity and performance of numerical algorithms (65Y20) Packaged methods for numerical algorithms (65Y15) Software, source code, etc. for problems pertaining to linear algebra (15-04)

Related Items (13)

Rational Krylov for eigenvalue computation and model order reduction ⋮ Data-dependent orthogonal polynomials on generalized circles: a unified approach applied to \(\delta \)-domain identification ⋮ Algorithms for the Geronimus transformation for orthogonal polynomials on the unit circle ⋮ GMRES algorithms over 35 years ⋮ A unification of unitary similarity transforms to compressed representations ⋮ Fast and accurate normalization of vectors and quaternions ⋮ Complex square root with operand prescaling ⋮ Implicit double shift \(QR\)-algorithm for companion matrices ⋮ Affine tensor product model transformation ⋮ Structured eigenvalue condition numbers for parameterized quasiseparable matrices ⋮ \(\mathbb G\)-reflectors: Analogues of Householder transformations in scalar product spaces ⋮ A unitary Hessenberg \(QR\)-based algorithm via semiseparable matrices ⋮ The Synthesis of Spatial Filtering Algorithm with a Constant Level of Useful Signal

Uses Software

• LAPACK
• EISPACK
• LINPACK

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